Problem: What do the following two equations represent? $-x-3y = -4$ $-x-3y = 4$
Solution: Putting the first equation in $y = mx + b$ form gives: $-x-3y = -4$ $-3y = x-4$ $y = -\dfrac{1}{3}x + \dfrac{4}{3}$ Putting the second equation in $y = mx + b$ form gives: $-x-3y = 4$ $-3y = x+4$ $y = -\dfrac{1}{3}x - \dfrac{4}{3}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.